(CNN) -- President Donald Trump said Saturday that he's considering a short-term quarantine of "hot spots" in parts of the tri-state area — New York, New Jersey and Connecticut — where cases of coronavirus continue to rise.
"We're thinking about certain things. Some people would like to see New York quarantined because it's a hotspot. ... We might not have to do it, but there's a possibility that sometime today we'll do a quarantine, short-term, two weeks on New York. Probably New Jersey, certain parts of Connecticut," he told reporters as he departed the White House.
"I'd rather not do it, but we may need it," said the President, who was on his way to Norfolk Naval Station for the sendoff of a Navy hospital ship to New York.
He later tweeted, "I am giving consideration to a QUARANTINE of developing 'hot spots', New York, New Jersey, and Connecticut. A decision will be made, one way or another, shortly."
New York Gov. Andrew Cuomo said that he spoke with Trump on Saturday morning, but that the two had not discussed a quarantine.
"I don't even know what that means. I don't know how that could be legally enforceable," the Democratic governor said during in a news conference in Albany. "And from a medical point view, I don't know what you would be accomplishing."
"But I can tell you, I don't even like the sound of it," he added.
Trump, however, said that possible quarantine would be "enforceable" and "restrict travel" from those parts of the tri-state area. He also said any quarantine wouldn't affect truckers from outside the New York area.
"Restrict travel, because they're having problems down in Florida, a lot of New Yorkers going down. We don't want that," he said.
Florida's governor had mandated a 14-day self-quarantine or isolation period for travelers coming to Florida from airports in New York, New Jersey and Connecticut.
As he departed from Joint Base Andrews, Trump said he would speak to Cuomo later about the possible quarantine.
He said that it would be "for a short period of time, if we do it at all" and that he would not close the New York City subway.
Earlier this month, Cuomo had deployed the National Guard and created a 1-mile "containment zone" in New Rochelle, a suburb of New York City, in an attempt to stop a growing cluster of coronavirus cases.
The National Guard helped coordinate delivering meals to those in quarantine and a drive-thru coronavirus testing site was opened.
Cuomo said that the number of new coronavirus cases slowed over the period the restrictions were imposed.
As of Saturday morning, New York had at least 728 reported deaths due to coronavirus and at least 52,318 reported cases — making it the state with the most reported cases in the US, according to CNN Health's tally.
Trump says he may invoke Defense Production Act this week
Trump also said Saturday that he plans to invoke the Defense Production Act "maybe once or twice" this coming week.
The President did not identify which companies or supplies he would use the order to produce, but he did suggest he was facing push back from companies he called "little problem children."
"We're look(ing) at two companies that have not lived up to what they said. I would say they're in the 1% group, okay? And all of a sudden they heard we're going to use it and they're rolling out the red carpet," he said.
The President invoked the DPA on Friday, requiring General Motors to begin making ventilators.